Last week the Congressional Budget Office released a study on a proposed minimum wage hike. Their conclusion was that raising the minimum wage by 39 percent from $7.25 to $10.10 would reduce employment by roughly 500,000 jobs. I appreciated this study, not least of all because in 2010 I published a study that concluded that the 41 percent increase in the minimum wage after 2007 cost the U.S. economy some 550,000 jobs.

The CBO study looked at all the peer reviewed economic research on the minimum wage, and combined it with labor force data to craft a simulation model on the effects of the proposed change. I built an historical model of changes in employment, controlling for the recession, trends, seasonal dynamics and demographics. We both came up with the same answer to roughly the same question.

This is not too surprising really. All economists know there is no such thing as a free lunch. While an increase in the minimum wage would boost earnings for many workers (a believable 16.5 million according to the CBO), it will also cost jobs. There’s really no honest way around these two conclusions.

Still, regardless of how you feel about the minimum wage, there are other troubling matters at stake. You, see our public policies towards low wage work muddle the debate enormously, and it is not really clear what the final effect has so far been.

The 1996 welfare reform extended Medicaid to the working poor and expanded Earned Income Tax Credit. The Medicaid expansion was designed to remove the biggest disincentive to work poor families faced – the loss of health care benefits. The second was designed to extend the progressive tax system into the ranks of the poor and so incentivize work.

Both of these policies worked, but there were side effects to government intervention in markets (as indeed, there always are). The greater availability of lower-wage workers meant that many firms crafted new business models designed around low-wage, low-skilled workers of which there was now abundance. For example, there was an 18 percent increase in restaurant employment from 1996 through 2001. It seems to me that businesses at this end spend less time training and nurturing workers.

As an aside, this is an example where moralizing is unhelpful. Both the decisions not to work in order to preserve family health care and the adjustment by businesses to a profusion of low-skilled workers are privately optimal. We should expect no more or less from our economic decisions.

So, the minimum wage debate has to be framed against the backdrop of Medicaid and EITC. If we raise the minimum wage to $10.10 then the better-paid households will need fewer benefits, while the newly unemployed will need more. We will have resurrected a barrier to work among folks who need fewer barriers to obtaining skills at a time when fewer employers have strong training programs. This is a fairly complex issue, but I feel certain the public debate will not be.